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Rationally Speaking is a blog maintained by Prof. Massimo Pigliucci, a philosopher at the City University of New York. The blog reflects the Enlightenment figure Marquis de Condorcet's idea of what a public intellectual (yes, we know, that's such a bad word) ought to be: someone who devotes himself to "the tracking down of prejudices in the hiding places where priests, the schools, the government, and all long-established institutions had gathered and protected them." You're welcome. Please notice that the contents of this blog can be reprinted under the standard Creative Commons license.

Friday, July 12, 2013

Progress in philosophy: the Gettier case

by Massimo Pigliucci

As I’ve mentioned now a number of times, I’m in the midst of writing a book for Chicago Press on whether and how philosophy makes progress. The short answers are: yes, but in a way that is different from how science makes progress. Specifically, I will be arguing that philosophy is concerned with possibilities in logical (as opposed to empirical) space, and that therefore progress is measured by the elimination of logically flawed positions and the refinement of logically sound alternatives. Since empirical space broadly underdetermines logical space, this also means that in some sense doing science is actually easier than doing philosophy — or at the very least that there are good reasons why philosophers don’t usually settle on one “correct” theory of anything.

This is all well and good, you might say, but can you please give an example or two? Yes, I can. In this post I will explore a particular instance of what I consider progress in philosophy, and specifically in epistemology — the full book will contain several more, drawn from subfields as varied as ethics and philosophy of science.

The example in question has to do with nothing less than the very definition of knowledge, and in particular regards what happened in that area of epistemology in the aftermath of a short paper (three pages) published by now retired University of Massachusetts at Amherst’s Edmund Gettier back in 1963 (as it turns out, he wrote it in order to get tenure, and it is the only paper he published in his entire philosophical career!).

The following may become a bit technical (and you may want to read other stuff about it, like this recent short article by Fred Dretske at The Philosophers’ Magazine), but bear with me, it's worth it.

So, beginning on the left side of my conceptual space, we start with the standard definition of knowledge — going back to Plato — as Justified True Belief (JTB). This means that for something to count as knowledge, the epistemic agent’s (e.g., you) belief about a certain matter has to be both true and (rationally) justified. For instance, let’s say you believe that the earth goes around the sun, rather than the other way around. This belief is, as far as we can tell, true [1]. But can you justify it? That is, if someone asked you why you hold that belief, can you actually give an account of it? If yes, congratulations, you can say that you know that the earth goes around the sun. Otherwise you are simply repeating something you heard or read somewhere else. (Which, pragmatically, is fine. It just doesn’t count as knowledge, that’s all.)

Now, the above approach was fine for about two and a half millennia, until some people — like Bertrand Russell — began questioning it and thinking about its limitations. But the big splash on the knowledge thing was the above mentioned short paper by Gettier. Because the problem posed by Gettier may not sound that impressive the first (or second) time you’ll actually look at the details (as we will do in a minute), let me remind you that, for instance, John L. Pollock and Joseph Cruz are on record as saying that it has “fundamentally altered the character of contemporary epistemology” and that it constitutes “a central problem of epistemology since it poses a clear barrier to analyzing knowledge.” So there.

Let’s get started with a typical “Gettier case,” that is a hypothetical situation that seems to be an exception to the JTB conception of knowledge. Let’s say I get letters, copies of utilities bills and other documents from my friend Phil, and they all refer to a residence in New York City, state of New York. I would be justified in believing that Phil lives in New York City. If Phil lives in NYC, then it is also true that Phil lives in the State of New York, and consequently I believe that too. Turns out, however, that Phil actually lives on Long Island. So my first belief about Phil was simply wrong. This presents no problem for the JTB account, since my belief only satisfied one of the two conditions (it was justified, but not true). The trouble comes when we assess my second belief, that Phil lives in the State of New York. I am correct, he does. That belief of mine is both true, and justified (logically, given the premise that Phil lives in NYC). But now we have a case of justified true belief that is actually based on false premises, since Phil does not, in fact, live in New York City. [You may want to re-read this before proceeding, first exposure to Gettier cases is often confusing, but once you get it, it hits you like a brick!]

Gettier cases have the general form of the example I just gave: they get off the ground because they are about logically entailed truths that happen to be derived via a belief that is justified but not true. The problem they pose is not with the first belief (the one that is justified but not true) but with the second belief (the one that is logically entailed by the first one, and which happens to be true). Now what?

The first response — the first move in logical space after Gettier’s own — was for epistemologists to seize on the fact that Gettier cases depend on the presence of false premises and simply amend the definition of knowledge to say that it is justified true belief that does not depend on false premises (the “no false lemma” solution, see figure). As it turns out, however, one can easily defeat this move by introducing more sophisticated Gettier cases that do not seem to depend on false premises, so called general Gettier-style problems.

Here is one possible (if a bit contrived) scenario: I am walking through Central Park and I see a dog in the distance. I instantly form the belief that there is a dog in the park. This belief is justified by direct observation. It is also true, because as it happens there really is a dog in the park. Problem is, it’s not the one I saw! The latter was, in fact, a robotic dog unleashed by members of the engineering team from Bronx High School. So my belief is justified (it was formed by normally reliable visual inspection), true (there is indeed a dog in the park), and arrived at without relying on any false premise [2]. And yet, we would be hard pressed to call this an instance of “knowledge.” It’s more like a lucky coincidence.

There is a move that can be made by supporters of the no false lemma solution to repair their argument, for instance adding that the epistemic agent needs to (consciously or even unconsciously) consider the possibility of both deception and self-deception, claiming knowledge only when those have been ruled out. The problem with that solution is that if we accept this then it turns out that we hold to a lot fewer justified beliefs than we think.

A related, but distinct, move, is to say that Gettier cases are not exceptions to JTB because it does not make sense to say that one can justify something that is not true. That may be, but this moves the discussion away from the concept of knowledge and onto the concept of justification, which turns out to be just as interesting and complicated (and outside the scope of this post).

A completely different take is adopted by philosophers who have tried to “dissolve” rather than resolve the Gettier problem (lower portion of the concept map). Here there are at least two areas of logical space that can be reasonably occupied: the minimalist answer is to bite the bullet and agree that all cases of true belief, including accidental ones, count as knowledge. The good news is that we end up having much more knowledge than we thought; the bad news is that it seems we are now counting as “knowledge” the sort of lucky coincidences (see the dog example above) that are really hard to swallow for an epistemologist. A second way of dissolving the Gettier problem is to say that it gets wrong the concept of justification (again, shifting the focus of the discussion). For instance, one could say that justification depends not just on the internal state of the epistemic agent, but also on how such state relates to the state of affairs in the external world (the dog is really a robot!). This means that we are now owed an account of why there may be a mis-alignment between internal and external states, or what makes a belief appropriate or inappropriate.

The center of my concept map refers to two broad categories of replies, one that adopts the strategy of revising the JTB approach itself, the second that aims at expanding it with a further, “G” (for Gettier) condition. Let’s start with possible modifications of JTB. One option was suggested by the above mentioned Dretske and separately by Robert Nozick, and is known as the “truth tracking” account: it basically says that the epistemic agent wouldn’t believe proposition P if P were not true. This immediately leads to the question of what accounts for agents having this or that belief, of course. A second modification of JTB is known as Richard Kirkham’s skepticism, and it is an acknowledgment of the fact that there will always be cases were the available evidence does not logically necessitate a given belief. This move in turn leads to a split: on the one hand one can simply embrace skepticism about knowledge and be done with it. On the other hand one can adopt a fallibilist position and agree that a belief can be rational even though it doesn’t rise to the lofty level of knowledge.

We now move to explore the last area of logical space opened up by discussions of Gettier problems: the so-called “fourth condition” family of approaches. One is represented by Alvin Goldman’s causal theory of belief, which says that it is the truth of a given belief that causes the agent to hold to a belief in the proper manner (an improper manner would fall back into Gettier-style cases). This again raises the issue of how we account for the difference between appropriate and inappropriate beliefs (the very same question we have seen raised by one of the dissolution approaches, the one that says that Gettier cases involve a wrong concept of justification, as well as by the Dretske-Nozick response). Goldman himself was happy to proceed by invoking some form of reliabilism about justification, a discussion of which will definitely lead us outside the territory being charted here.

Keith Lehrer and Thomas Paxson have advanced the possibility of defeasibility conditions: knowledge gets redefined as “undefeated” justified true belief. The problem here is that it is hard to get a good grasp on the concept of a defeater in a way that it doesn’t rule out well established instances of a priori knowledge (like logical and mathematical knowledge).

Finally, we have the pragmatic move: since truth is defined by pragmatists like Charles Sanders Peirce as the eventual opinion reached by qualified experts, we get that in most ordinary cases of “knowledge” we simply need to embrace a Socratic recognition of our own ongoing ignorance.

Now, you may be thinking: so, after all this, what is the answer to Gettier-style problems? What is the true account of knowledge? If so, you missed the point of the whole exercise. Unlike science, where we do seek answers to questions determined by empirical evidence, philosophy is in the business of exploring possibilities in logical space. There are often many such possibilities, since the constraints imposed by logic are weaker than those imposed by empirical facts. At the end of this sort of discussion we are left with the following: a) A much better appreciation for the complexities of the deceptively simple question: what is knowledge? b) An exploration of several possible alternative accounts of knowledge and related concepts (such as justification and belief); c) A number of options still standing, some of which may be more promising than others; and d) A number of possibilities that need to be discarded because they just don’t work when put under scrutiny. And that, my friends, is how philosophy makes progress [3].

__________

[1] Yes, yes, I know that it’s not really the case that the earth rotates around the Sun, as much as that the Sun occupies one of the foci of the elliptical orbit of our planet (the Newtonian account). Or better yet, that both Sun and Earth interact in a complex fashion because of their respective gravitational fields (the relativistic account). But all of this is largely irrelevant to the point I’m making here.

[2] Notice that the premise that my observations are reliable under normal conditions is not false.

[3] It’s also possible that you may be asking yourself which of the above options I think is the best. Well, my thinking at the moment is that JTB is ok as a first approximation — that is, any time you are not talking to professional epistemologists. Of the others, I’m ok with responses that invoke either fallibilism or reliabilism, which means that I can go either with Kirkham’s skepticism or with Goldman’s causal theory. Then again, philosophers of knowledge may not be done just yet exploring the relevant logical space...

59 comments:

This problem of progress definitely parallels the same problem in science though, don't you think? You have a well established and consensus-supported position/programme, overturned/falsified by a 'bold' test, and in the aftermath you have more questions than you started out with. Insert 'newtonian physics' for the programme and you're talking about progress in science, swap it with "Platonic Justified True Belief" and you move into philosophy.

Not a criticism, obviously, since you off the bat note there are parallels, and of course "Popperian Falsification" isn't the be all/end all of scientific knowledge.

Philosophy is not about "possibilities" as you state but rather about truth, the absolute, what IS.

As for the definition of knowledge, knowledge is thought, be it true or not. Wisdom IS truth, the single absolute.

Beliefs are like scientific theories and religious faiths, quantum mechanics and the Easter Bunny, only probable at best.Truth actually or really IS.

If you are going to build your knowledge be it philosophical, scientific, or religious, on anything, I would suggest you start with IS.Or as Thoreau would say: "If you have built castles in the sky Let not your dreams go to waste; Just build the foundations under them."

> This problem of progress definitely parallels the same problem in science though, don't you think? <

Not exactly. Science makes progress by exploring empirical space, which is much more constrained than logical space. This in turn means that often progress in philosophy doesn't look like progress, because philosophers identify a number of logically consistent / adequate solutions but not a uniquely valid one. It is progress nonetheless, once one recognizes the differences in methods and subject matters.

Vasco,

> how is there a problem in recognizing that in fact “it turns out that we hold to a lot fewer justified beliefs than we think”? <

Well, if one bites the bullet and adopts some of the proposed responses to Gettier one ends up with a *lot* less or more "knowledge" than is commonly accepted. Before doing that, one needs to weigh whether the new account of knowledge doesn't distort so much our concept as to be unacceptable.

I'm interested in the way Massimo is using the word progress. Progress in science is pretty obvious, and, in the popular mind, is associated with increasingly powerful technologies. There is clearly progress on the technological front and, as technologies ultimately derive from scientific discoveries etc., scientific progress can reasonably be inferred.

This notion of progress is fairly straightforward. There is a clear going-forward, a pattern of improved techniques based (presumably) on a better and constantly expanding knowledge base.

The sort of conceptual refinement Massimo is calling (philosophical) progress can also be seen as a form of progress. To a point.

For such discussion can and often does (in my experience) become a kind of competitive intellectual game indulged in for its own sake. The original problem or point of the discussion is more or less forgotten or obscured.

I enjoyed reading the article and fitting my views into the framework Massimo presents here. But I just have the sense that there comes a point where going deeper into the ramifying complexity of possibilities does not necessarily entail going forward.

The Gaultier problems show us that there are a few (or a lot) of beliefs that we assume as trues that in fact are not (mostly for not being correctly justified).

Knowing that (and what) we don’t know is progress by itself, as it gives a better correspondence with our knowledge to reality. The dismissal of (our) ignorance is quite foolish.

Even in science, significant progress in knowledge alwasy leads to new questions (the things we know that we do not know), although this is common knowledge many people wrongly assume that this is just rhetorical, which is not the case. In fact, in the process of realizing that we do not know, it happens we learn of lot (and that is our knowledge).

For instance, let’s say you believe that the earth goes around the sun, rather than the other way around. This belief is, as far as we can tell, true. But can you justify it? That is, if someone asked you why you hold that belief, can you actually give an account of it? ... Otherwise you are simply repeating something you heard or read somewhere else. (Which, pragmatically, is fine. It just doesn’t count as knowledge, that’s all.)

That appears to be a bit too narrow a definition. Surely I can "know" something from reading it somewhere else even if I do not understand all of the details of why it is true or even only how it has been found out. E.g., I know that Manila is the capital of the Philippines although I have never been there. It is simply a reasonable assumption that the authors of all those maps and books would not gain anything by lying to me. Not having to generate all knowledge myself is kind of what we have experts for, and by that strict standard there would be very, very little knowledge in any individual person. Basically you would gain hardly any knowledge from primary school because you rarely do experiments or prove theorems at that stage.

there are good reasons why philosophers don’t usually settle on one “correct” theory of anything.

Don't get me wrong, I do believe that philosophy can make progress as a matter of principle. However, as a matter of practice, it is surely a greater problem than this comment acknowledges that philosophers so rarely settle issues. For some reason there are much larger minorities of professional philosophers than of professional scientists holding views relevant to their field that should by any reasonable standard be considered discarded. (Seriously, 27% for non-physicalist mind? Are they kidding or do I misunderstand what that means?)

"In the philosophy of logic, the natural language connectives ‘and’, ‘or’, ‘not’, and ‘if ... then’ are widely discussed and so are their formal counterparts, such as the truth-functional connectives of classical logic or counterfactual and strict conditionals in modal systems. Considerably less attention has been paid to the explanatory connective ‘because’."

"Because" is indicative of purposes, as in 'because that was its purpose,' or 'because that's the purpose that it served.' Massimo's purpose to write a book on knowledge without purpose will be an interesting example of whether purpose can be purposefully ignored successfully.

I always felt Gettier problems led me to the assumption that when we look for "necessary and sufficient conditions" as a definition we should expect failure. I guess that puts me in the (a) camp. Some of my favorite papers about this took the form of "How to make your own Gettier counterexamples".

Still, I do like a story about a guy who received tenure by writing a three page paper full of counterexamples.

> I would say that "logical" space does not exist does not exist, but "conceptual" space (the other space mentioned here and is a brain thing) does <

I disagree, since we are talking about concepts that hold up to logical / rational scrutiny. But sure, if that's the way you feel more comfortable putting it, let's talk about conceptual space. (After all, I did use a concept map in the post to track responses and criticisms to Gettier-style problems.)

Seth,

> Isn't philosophy similar in that it progresses by helping our beliefs to become 'better justified'. I guess I am advocating the pragmatic approach <

Yes, I'm sympathetic to that approach too, especially within the context of reliabilist and fallibilist considerations.

Mark,

> There is clearly progress on the technological front and, as technologies ultimately derive from scientific discoveries etc., scientific progress can reasonably be inferred. <

Well, yes, but it's more complicated than that. A lot of scientific progress has little or no technological import, and there are entire fields (ecology, for example) where sometimes it is difficult for the practitioners themselves to tell whether there has been progress and in what sense.

> For such discussion can and often does (in my experience) become a kind of competitive intellectual game indulged in for its own sake <

Trust me, that happens in all academic fields, scientific ones not excluded.

> I just have the sense that there comes a point where going deeper into the ramifying complexity of possibilities does not necessarily entail going forward. <

I agree, but I have read plenty of scientific papers at the end of which I wondered: why did they bother with this?

> Knowing that (and what) we don’t know is progress by itself, as it gives a better correspondence with our knowledge to reality. The dismissal of (our) ignorance is quite foolish. <

I agree with the latter sentiment. I'm not sure if your comment about knowledge of reality referred to progress in philosophy. If so, the issue is that philosophy is not (primarily) concerned with empirical reality (that's the job of science), but with logical / conceptual possibilities. In which case any talk of "correspondence" is beside the point.

Alex,

> Surely I can "know" something from reading it somewhere else even if I do not understand all of the details of why it is true or even only how it has been found out. <

Not if knowledge is justified true belief. We are talking about the technical sense of "knowledge" in philosophy, not about the everyday understanding or usage of the word.

> you would gain hardly any knowledge from primary school because you rarely do experiments or prove theorems at that stage <

I don't think that's the issue. The JTB concept of knowledge doesn't require, say, you to do experiments in fundamental physics in person in order to claim knowledge that electrons have certain properties. But it does require you to be able to provide an explanation of why physicists believe certain things about electrons.

> For some reason there are much larger minorities of professional philosophers than of professional scientists holding views relevant to their field that should by any reasonable standard be considered discarded <

I hear you, but from the perspective I'm suggesting this should not be surprising. Non-phisycalism, for instance, is a tenable position in logical space, especially if defined / refined in certain ways. It is even tenable to entertain the possibility that we are all part of someone else's computer simulation. Of course I do not think for a minute that all logically tenable positions are equally viable, but that's why philosophical inquiry is more difficult and leads to a wider variety of opinions among practitioners than scientific inquiry does.

Philip,

> one uses logical + empirical methods to understand physical space. Logical methods in understanding conceptual space could be philosophy, but all these could overlap and mix. <

Yes, formal logic is an obvious example of a sub discipline of philosophy in which there is progress. And yes, of course there is an overlap between logical and empirical inquiry, and therefore between philosophy and science. I think of the two as two distinct yet partially overlapping peaks in a broader intellectual landscape (a landscape that, let's not forget, includes also mathematics).

jermox,

> do like a story about a guy who received tenure by writing a three page paper full of counterexamples <

Right? Not to mention that that was his only contribution to the field in his entire career!

I was not addressing the "knowledge of reality", but the knowledge (the beliefs) per si and its correspondence to reality (what is true). And I think that the knowledge of what we do not know constitutes progress (in philosophy, science, ...).

I would like to add that we can not honestly overcome the Gettier problems, as you said try to “dissolve rather than resolve the Gettier problem”.

Logical possibility is a rather low hurdle to clear. When philosophers are asked what positions they hold they can be expected not to answer with some stance drawn randomly from logical space but with what they consider to be most plausible. If we then find that large groups of philosophers hold mutually contradictory positions then it would appear as if either there is no way of deciding on the plausibility of each of them or (and that would be the option I consider more likely to be true) as if philosophers are not really forced to give up implausible positions, perhaps simply because there is no incentive to do so. For example, even if a philosopher is demonstrably wrong about metaphysics that does not cause airplanes to crash, companies to go bankrupt or experiments to fail. In the worst case, they are criticized by other philosophers.

Not really, as the history of the debate about Gettier-style problems clearly should show.

> even if a philosopher is demonstrably wrong about metaphysics that does not cause airplanes to crash, companies to go bankrupt or experiments to fail <

My friend, that's true also for a lot of science, which is also largely inconsequential, despite the contrary mythology that so many scientists cling to, largely because without it they would have to explain to society why we spend so much money to fund so much studies into irrelevant topics.

Baron,

> Massimo's purpose to write a book on knowledge without purpose will be an interesting example of whether purpose can be purposefully ignored successfully <

As usual, you make precisely no sense. When did I ever say that the notion of progress in philosophy and other disciplines (which is what the book is about) is independent of the purposes of philosophers and other academics? When did I ever say that human beings don't have purpose?

When did you ever say there was any value in thinking about philosophical progress in terms of purposes as Peirce suggests?"In the pragmatic way of thinking in terms of conceivable practical implications, every thing has a purpose, and its purpose is the first thing that we should try to note about it."

Not just of humans but of every thing, right? But as a matter of fact you've never said that even human beings have other than their illusions of a purpose, and as to other beings that philosophy can't at least reliably ignore, you've never seen them serving any of our purposes, or having any of theirs, except by seeing accidents as purposeful. Worse, you see no purpose at all in evolution, either of our biological forms or of the natural history and its laws that "accidentally" gave rise to them.

My friend, that's true also for a lot of science, which is also largely inconsequential, despite the contrary mythology that so many scientists cling to, largely because without it they would have to explain to society why we spend so much money to fund so much studies into irrelevant topics.

I was careful to include "experiments fail". Even in topics that you might consider "irrelevant", which would perhaps include what I work on, somebody in five or ten years will try to build on it and, because they will be studying the same world as I am now, they will find out if I claimed something that is demonstrably wrong.

But the real question is: DO philosophers as a class really give up on propositions that one of them has shown to be illogical? It seems as if much larger percentages of them continue to hold illogical positions than scientists continue to promote superseded theories. And if that is so, why is it so?

I must take a contrary view to the idea that it makes sense to speak of "philosophy" as making progress.

It makes sense to speak of science making progress because science is chartered on the basis of more or less objective goals - i.e., knowledge of a certain kind about certain domains of reality - that it gets closer to or does not. Here by an "objective" goal I mean one that isn't open to reasonable debate outside a certain narrow range.

It does not make sense to speak of philosophy making progress because philosophy has no objective goals. Individual philosophers may have goals, but none can say that their goal is THE goal of philosophy without a bit of arrogance, not to mention being wrong.

Supposing it were objectively true that the goal of philosophy were knowledge of a certain kind, there still may be enormous reasonable variation on the question: knowledge of what? This is largely a matter of value after all. To say that THE goal of philosophy is metaphysical knowledge, for instance, is as arbitrary as saying its knowledge of music. Both may be worthy philosophical goals, but it is nonsense to say that either (or both) are THE, or some of THE, goals of philosophy.

But it's not even objectively true that the aim of philosophy is knowledge. There are and have been philosophers who take something other than knowledge as the focal point of their philosophy. These might be wisdom, understanding, a certain way of life, inner peace, good relationships, and so on. (Let's not even bring religion into the matter.)

So because philosophy has no necessary, shared, objective goals, it makes no sense to speak of philosophy as making progress: progress with respect to what? There are only individual philosophers and schools with their own idiosyncratic goals with respect to which they do or do not make progress with; and for any of them to elevate their own philosophical goals to THE goals of philosophy is, again arrogant, a kind of mad cultural imperialism perhaps.

Philosophy is more like poetry than science in that it admits of an endless range of differing, valid personal projects within it such that it makes little sense to speak generally about what the enterprise is about. Those who do are like poets who say that poetry is necessarily about love, or God, or what have you.

And even if we limit the conversation to academic philosophy, which at best is a particular school, or set of schools, of philosophy, it's still problematic to see the goals of philosophy as objective. Do we want philosophy departments wherein it's assumed that what philosophy is about is a closed question? While such narrowness may be a requirement in science, in philosophy it's dogmatism at best. Because that question can't be closed, we can't speak of objective goals of philosophy, and hence we can't speak of the progress of philosophy in a general sense; when we do we're just speaking about own philosophy in a quasi-objective way.

Gee, here I get Massimo to at least agree that philosophers either have or serve a purpose, and this guy claims there are no objective goals that such purposes could serve. How about subjective goals, do they count?

I mean that you seem to have no idea what a goal is, objective, subjective, or what's always some combination of both. I mean that if anything I've read didn't have an objective goal, it would be your present argument, and yet, subjectively, to you it has.

One day Paul I hope you find the objective world equal to the subjective world and in this light see the progression of philosophy the Way toward truth the Oneness of absolute.Einstein said that of all the groups he would most wish to associate with it would be the true searchers, but that there were only a few living at One time.Be One too,

I'm absolutely sure that the goal of philosophy has been stated - or discovered - long ago, perhaps by Socrates, and it is named after one of its said disciplines, I mean, Ethics. In short, is THE GOAL itself...

But it can't prevent itself from investigating other subjects, as they prove crucial to this accomplishment, like Knowledge, for instance. To me knowledge is synonym to being (in this particular I follow a very crazy man, considered by some philosophers as one of them, called Boehme). Is there a moment in our lives in which we are not knowing (in the broadest and only sense, naturally)?

I agree with you that it does make sense to think of philosophy as making progress, and that this progress takes the form of (a)making certain positions untenable (b)proposing new tenable positions.

As for the specific discussion of knowledge, I have a few points to make.

Should we expect that there be a right definition of knowledge? The concept of "knowledge" is just an instinctive human intuition, and any definitions philosophers come up with are simply attempts to pin down what's a bit vague and nebulous to start with. But if it's so vague, then perhaps we should not expect to be able to find a precise definition that matches all corner cases. It's like trying to define music, or art.

For example, in your Gettier case example, the question of whether you "know" there is a dog in the park is not fundamentally a terribly interesting one to me because it is just a semantic question. It depends only on how you define knowledge, and settling the question will not reveal anything about reality but instead allow us to adopt a useful linguistic convention.

I think there's a weakness in this particular example, however, as your knowledge is actually based on a false premise.

Premise1: If it looks like a dog, it is a dogPremise2: I see an object that looks like a dog in the park

Premise2 is correct, but Premise1 is incorrect. Your belief that there is a dog in the park is therefore not justified.

Ultimately, I'm not convinced that knowledge is a useful foundational concept. Once we have concepts of beliefs and truth, I'm not sure knowledge adds much but confusion when we get to these unusual cases, and this is probably because "justification" is too vague - what appears justified to me may not to you.

This short introduction to the topic treats justification as a boolean true or false proposition, whereas in reality beliefs are not simply justified or unjustified but justified to a greater or lesser extent. Premise1 is true in 99.9% of cases, perhaps, but not true in all cases, so any conclusion based on this premise is not completely justified.

And there are other differences of interpretation - for example, I may think that it is perfectly justifiable to believe that a hydrogen atom has one proton because I read it in a science book, and I know that scientists don't make claims without evidence. You may be of the opinion (as you seem to be) that this is not justifiable unless I learn about the experiments that lead to this discovery. There is no way to settle this question objectively, so no way to decide what counts as knowledge even in this very typical non-Gettier case.

Another example: since all justifications for knowledge must ultimately rest on premises, what's to stop me from jumping the gun and basing my beliefs on arbitrary premises that may or may not be true? For example, suppose I adopt the premise that there is a teapot orbiting Pluto. From this, I can conclude that there is an item of crockery to be found in the far reaches of our solar system. Now, if it so happens that there is actually a teapot orbiting Pluto, can it be said that I knew that an item of crockery could be found in the far reaches of the solar system? It seems not - therefore you can't start your reasoning from arbitrary premises. Your basic premises must be justified to some extent. But since all reasoning must start at some basic foundational premises, then there can be no ultimate justification.

In my view, knowledge should be regarded as a useful shorthand for the typical cases. The colloquial usage is fine - any attempt to define it more rigidly than JTB is futile (unless perhaps the adoption of a specific definition is useful for the purposes of a particular discussion).

Finally, I'd like to agree with Alex that it is perfectly philosophically acceptable to claim to know the capital of the Philippines is Manila. In many many cases, the only justification you need is a source - to say that you know something because somebody told you. All you need to do is adopt the premise that the source is reliable. If the premise is true, then any beliefs you form from trusting the source will be justified.

If, however, you believe that the earth was created in seven days because you read it in Genesis, then you are basing your beliefs on false premises, so this would not count as knowledge.

Strikes the eye in Gettier's paper the first note, where he states: "Plato seems to be considering some such definition at Theaetetus 201, and perhaps accepting one at Meno 98". Seems? Perhaps? In fact he tried to validate it, although he had no sufficient competence (who would have it?) to do it. His problem and of those who aligned themselves with his inconclusive argument seems to be the cracking of the whole process of knowing, leaving behind its start point, perception, as if it could happen in the absence of thought. Another issue is to believe that the ability to think is something different from the senses it coordinates: I hold the thought as our 6th sense. And so knowledge is perception from start to end, although perception compared or put against other perceptions in order to make sense of the world: theories, logical spaces etc are what the thought gets from all that goes inside itself (what results from this process of collation), which means that they are perceived as well (and so, are real, I mean, not transcendent). Then, it seems that there's no magic formula to get to the perfect theory, the world viewed from a single set of ideas or propositions, although we insist either in believing in or in seeking them. Even if the world wasn't changing all the time, as observers we would be seeing it from distinct points of view (if not this, we would be one an only being, watching from a single spot), which means: as single individuals we're not able to infer much, because all tha data we have are incomplete, and as a group the issue comes from the difficulty of making converge our different experiences ( due to language, disputes etc). And knowledge, like truth, is by necessity relational, this meaning that we are committed to consider whatever else that exists beyond or inside the object we are observing in order to know it, having beforehand the certainty that in itself or by itself no object is likely to be known.

This kind of litany is exhaustively repeated by early philosophers while trying themselves to overcome those limitations: didn't I even read some of Gettier's arguments in Thaetetus (I'm not sure, but I'll check)? So. Progress in philosophy? In my view we're trying to reinvent the wheel, but a complicated one, on the verge of the uselessness. Difference between philosophy and natural sciences? Well, if we understand that the data from the senses are processed elsewhere, not in our brains, perhaps: again, the problem is to find out the adequate correspondence between world and its symbols, as Peirce tried to show; is to keep control of our thinking in order that our mental processes don't go in a different direction from that of the facts.

Today is Derrida's birthday. (Some say he just wrote gibberish, but I don't think so.) I think he would say philosophy and science both make progress or both don't make progress (but not one and not the other). I think the former.

> Even in topics that you might consider "irrelevant" ... somebody in five or ten years will try to build on it and, because they will be studying the same world as I am now, they will find out if I claimed something that is demonstrably wrong. <

No, my experience is that much science simply doesn’t get replicated at all and that most “bricks of the edifice of knowledge” actually lay unused in the backyard, as John Platt famously wrote (in his “Strong Inference” paper, Science, 16 October 1964). But of course you do have a point: potentially experimental or empirical results can be checked and overthrown. However, that’s true also for analyses in logical / conceptual space, except — again — that there are more acceptable / coherent possibilities in the latter than in the former case.

> DO philosophers as a class really give up on propositions that one of them has shown to be illogical? <

“As a class”? That’s a funny way to put it. But yes, I do think so, by and large (especially if one excludes theologians from the ranks of philosophers, and understands that continental philosophy is actually a significantly different beast from standard and analytical philosophy). Indeed, I don’t know many philosophers who actually hold downright illogical views.

> It seems as if much larger percentages of them continue to hold illogical positions than scientists continue to promote superseded theories. And if that is so, why is it so? <

Again, not illogical, but yes, I said in the post that this is the case, and provided an explanation: conceptual space is much more vast and underdetermined by empirical evidence than the type of space in which science operates.

Paul,

> It does not make sense to speak of philosophy making progress because philosophy has no objective goals <

I couldn’t disagree more. Philosophy has many goals, and I don’t see why they wouldn’t be objective. The case in point, a better understanding of the concept of knowledge, is an obvious one. Or take philosophy of science, which has a number of goals, including but not limited to a rational account of the operations of science.

> none can say that their goal is THE goal of philosophy without a bit of arrogance <

That’s a sophistic point, if you don’t mind the quasi-insult. Nobody said that philosophy has *one* goal, but it doesn’t follow that there are no objective goals within subfields of philosophy (as argued above). And this variety shouldn’t be surprising, since philosophy has always been a meta-field, preoccupied with nothing less than the whole of human knowledge and understanding.

> because philosophy has no necessary, shared, objective goals, it makes no sense to speak of philosophy as making progress: progress with respect to what? <

With respect to whatever sub-goal some philosophers aim at, like a better analysis of the concept of knowledge in epistemology. There is an analog in science: ecologists don’t make progress in the same sense, or according to the same criteria, as fundamental physicists make progress (though I concede that the goals of science are more homogeneous than those of philosophy; but that’s only because science is more narrowly focused than philosophy).

> Philosophy is more like poetry than science in that it admits of an endless range of differing, valid personal projects within it <

Ah, that sounds to me like a good definition of some postmodern philosophy, which I barely recognize as part of philosophy proper...

I wouldn't have a problem with saying that this or that subdiscipline of philosophy makes progress - those are what I meant by particular projects within philosophy that can make progress. My problem is with the notion of philosophy as whole making progress. Even assuming it makes sense to speak of philosophy as having many goals, my concern remains. To speak generally of philosophy making progress one must have some subset of those many goals in mind, and that risks identifying philosophy with that narrower set of goals. What bothers me about this is that it suggests a dismissal or demotion of much of what has counted as philosophy on this planet. One may not like postmodernism, "neo-scholasticism,' Buddhism, religious and mystical philosophies, and so on, but it is philosophy - someone else's philosophy. If one acknowledges this variety of philosophy, speaking generally about philosophy making progress suddenly ceases to make as much sense. So I'm concerned that philosophy is being identified with a certain narrow horizon of philosophical concern and the rest dismissed as non-philosophy. While it's consistent with the philosophical spirit to regard other philosophies as junk, it is inconsistent with the philosophical spirit to narrowly limit what counts as philosophy to one's own philosophical orientation, which what is what I'm worried you're doing in speaking of philosophy in general as something to narrow enough to be such that talking about it making progress makes sense.

> I get Massimo to at least agree that philosophers either have or serve a purpose <

this is why I rarely answer your comments: do you seriously think I would deny that human beings (of which philosophers are a sub-set) do not have purpose? Did I not say to you countless times that humans (and possibly other similarly-brained beings in the universe) do have purposes? How many times do I have to state the obvious to you?

Disagreeable,

> Should we expect that there be a right definition of knowledge? The concept of "knowledge" is just an instinctive human intuition, and any definitions philosophers come up with are simply attempts to pin down what's a bit vague and nebulous to start with. <

Yes, but that can be said for any human concept, and it is surely useful to attempt to better articulate and refine our concepts as needed. After all, that’s how we make sense of the world.

> in your Gettier case example, the question of whether you "know" there is a dog in the park is not fundamentally a terribly interesting one to me because it is just a semantic question. <

Careful not to confuse the specific example (which is not inherently interesting, it is simply meant to be didactic) with the broader point of whether or not there are cases that defy the JTB concept of knowledge.

> This short introduction to the topic treats justification as a boolean true or false proposition, whereas in reality beliefs are not simply justified or unjustified but justified to a greater or lesser extent. <

Agreed, but notice that you have now moved the discussion from knowledge to justification. As noted in the post, this is a possible move in the conceptual space identified by the JTB-Gettier debate.

> You may be of the opinion (as you seem to be) that this is not justifiable unless I learn about the experiments that lead to this discovery. There is no way to settle this question objectively, so no way to decide what counts as knowledge even in this very typical non-Gettier case. <

Not sure why you would count hearsay as knowledge. Epistemologists certainly don’t, and this is an example of a technical discussion within a specific field of philosophy. If you reject the JTB itself then of course none of what I wrote is relevant to you. But you’d be at odds with the entire epistemology profession.

> therefore you can't start your reasoning from arbitrary premises. Your basic premises must be justified to some extent. But since all reasoning must start at some basic foundational premises, then there can be no ultimate justification. <

All of this is correct, but I don’t see what it has to do with the discussion at hand. “Justification” in this context is clearly limited to whatever it is that we are debating (say, the notion of a teapot orbiting Pluto), it is not a meta-philosophical discussion on foundational knowledge. We can have that discussion too, but it would proceed along very different lines.

> In many many cases, the only justification you need is a source - to say that you know something because somebody told you. <

You are using the colloquial sense of “knowledge,” not the technical one.

Waldemar,

> knowledge is perception from start to end <

So you perceive mathematical objects and that’s how you arrive at mathematical knowledge?

@Massimo: "this is why I rarely answer your comments: do you seriously think I would deny that human beings (of which philosophers are a sub-set) do not have purpose? Did I not say to you countless times that humans (and possibly other similarly-brained beings in the universe) do have purposes? How many times do I have to state the obvious to you?"Yes, in the long ago beginning you denied that anything, including humans, had a purpose. But what's more important, you have just denied again that anything other then humans or similarly brained beings have a purpose. (Which I note is quite similar to your opinions about intelligence.)So here's another comment to which your answer is expected to be rare: How does purpose kick in to a brain that otherwise did not evolve with the brain-like functions of that brain user's ancestral forms? Was it naturally selected by the purposelessness of accident, just as intelligence was supposedly selected by the natural selection process? Or is that a scientific question that philosophy has no requirement to be concerned with?

Thanks for your observation. I'd say yes to your question, provided we assume that the thought - I'm not even referring the brain, because it would be too obvious - is a function of perception and finally perception itself: it results from perceptions, coordinates the data senses collect from reality, and even perceives - no quotes, please - that which it processes. I've just watched 'The singularity is near', a very interesting movie, mostly because I finally found another advocate for this cause, Marvin Minsky, who states that there's no distinction between emotions and thinking (rational including), a position severely defended by Argentinian/Brazilian Neurology researcher in memory, Izquierdo. I use to conceive the thinking as an ability one of whose characteristics is to perceive itself, like in a mirror: whenever we want we are able to say 'wow, I'm thinking!': this line of ideas is at least undertaking robots that soon will pass Turing test, for sure (the referred movie shows a scene in which Kurzweil's bot, Ramona, is uncovered after a remarkably long chat in 'Second Life', the game).

And perhaps, considering the thought as a function of perceptions working itself as perception is methodologically useful, as for the mathematics is useful - until a certain point - to think the series of positive integers' reason is the number 1. I don't see where this cracking of thought into perception (senses) and thought itself is useful beyond the selfish assumption that there are people that 'just' use their senses to live: I can't just conceive senses without thinking, as I said before.

I used two terms without interlinking them: perception and emotion. The latter is a kind of response the thinking ability - or the brain - attaches to whatever is perceived, its own work included. I believe that after a certain age we start to forget that the first real ideas we have from objects are emotions, which essentially refers our 'taste': likes and dislikes. This is the innate knowledge Epicurus and Epictetus refer to: and they don't overstate it!

The first ideas we have are instinctive reactions, instinctively directed choices based on behavioral strategies that our ancestors had learned and managed to pass on - in ways that evolutionists still fail to fully understand. But they do come from what has been loosely called our emotional brain, and again because we've not been able to give it due credit for its cognitive processing functions. Science has tried to monitor the physical processing of instinctive thought, but philosophy has so far failed to ascertain how instincts have evolved without conceding that at some point in our ancient pasts they had to have been intelligently and purposefully learned.

I know you are addressing Massimo, and without trying to enter in your discussion, but I think you go too far in your argument, in saying that “knowledge is perception from start to end”. Although it isn’t possible to dismiss perception when talking about knowledge, as here, when dealing with beliefs (in particular), but I think it is not possible (and reasonable) to reduce the issue just to perception (even if it would be possible and reasonable to speak about the relation between distinct perceptions, which wouldn’t make it very different, it would be just semantics). But, I may have missed your point.

No problem, Vasco, it's always a pleasure to chat in group. I could have approached the problem a little more smoothly than I did, but I intended to 'sting' Massimo a bit. Anyway, I take it seriously, first, from my own suspicions, second, after reading Epictetus (who states boldly that the good is the innate knowledge - boldly, I mean, plenty of arguments). As a matter of fact, I don't see any problem in recognizing the ability of thinking as a kind of perception or even the real, the true perception (as I'm sure no one would be able to imagine the senses working by themselves, without the coordination automatically done by the thoughts - the brain). After reading some of Vernant's works, notably on history of the idea of work in Greece and on Greek society and its philosophy, I realized a different way to understand the reason Plato (and perhaps Socrates himself) created that scission inside an activity as entire as the thought (I'm not telling that this whole can't be analytically split like any other object): maybe they were trying to signal to the people that their (people's) knowledge about certain things were incomplete, maybe just exercising their intellectual vanity towards people's common sense. I'm sure that the so called 'Minor Socratic' philosophers made a philosophy as good as the 'Major Socratic' ones' and it's really a pain to philosophy that so few of their works survived. Perhaps due to the fact that it has been taught in the streets (stoa),for instance, the Stoic thinking looks more useful, more pragmatic than the academic. Similar things can be said of Epicureanism: those philosophers got straight to the point without leaving behind the analysis of each problem their major statements entailed. The assumption about sense and emotion as knowledge (judgment) is one of them. Finally, some psychologists tried in the 90s to trace what they identified as the subconscious in which they included the data coming from the relatively autonomous set of neurons in the limbs and other organs: it's obvious we think differently when we have a heartburn, although we don't know - be it philosophically or 'scientifically' - what that really means. :)

Philosophy must take critically the assumptions behind what it understands by knowledge if it wants to disentangle several knots in this area and really progress! Most of times modern philosophy looks to me like a huge, massive row of embellishments made over early philosophy - I suspect bad reading... perhaps just preconception or even vanity. :(

Massimo:>Yes, but that can be said for any human concept, and it is surely useful to attempt to better articulate and refine our concepts as needed.<

Agreed to a point, however there are concepts that are vague and ill-defined, such as "soul", and there are concepts which are very precisely defined, such as "two". All the effort going into developing a precise definition of knowledge may be misguided if it's more like the former (in the sense that there is no precise meaning to uncover) and less like the latter.

For example, from the JTB point of view, I think "truth" and "belief" are relatively clear, and "justification" is the problematic concept which makes knowledge itself impossible to pin down.

>Careful not to confuse the specific example [...] with the broader point<

I'm not. I mean this question and the class of questions to which it belongs, namely questions which hinge solely on how we define a word.

>Not sure why you would count hearsay as knowledge. Epistemologists certainly don’t, and this is an example of a technical discussion within a specific field of philosophy.<

I'm not sure this is correct. Firstly, you're characterising knowledge based on the consensus of reliable experts as "hearsay", which is not reasonable. I'm agreeing with JTB but disagreeing with you on what it takes for something to be justified.

Going back to Alex's example, I would ask you whether you "know" that Manila is the capital of the Philippines. If you do not, then what would it take for you to know it? If you do, then is this not equivalent to what Alex and I propose as knowledge justified by what others have said and written, i.e. hearsay?

>If you reject the JTB itself then of course none of what I wrote is relevant to you<

I don't reject it, I support it. However I maintain that the concept of knowledge is a useful abstraction that covers typical cases and we should not be surprised if it breaks down or becomes imprecise in more unusual cases, just as Newtonian physics is perfectly adequate and correct for its domain but doesn't work at very small scales or very high energies.

For the typical day to day use of the term, JTB is an adequate definition. Where JTB doesn't work, the concept of knowledge is probably meaningless and it would be more helpful to ask what an agent believes than what an agent knows.

>>> In many many cases, the only justification you need is a source - to say that you know something because somebody told you. <<

You are using the colloquial sense of “knowledge,” not the technical one.<No, I'm using JTB. I'm asserting that being told a fact by a reliable source can confer justification, particularly when that information is corroborated by other sources. In your own example, you trusted your eyes to correctly report the sight of a dog. How is this different from trusting a very reliable source who informs you of the presence of a dog?

> What is truth Professor, would you answer like Socrates with only another question, or simply tell it like it really is? What is? <

Maybe you missed it, it was a recent post:http://rationallyspeaking.blogspot.com/2013/06/theories-of-truth.html

Disagreeable,

> there are concepts that are vague and ill-defined ... effort going into developing a precise definition of knowledge may be misguided <

Agreed, but this is a point recognized by a number of philosophers since Wittgenstein. Indeed, my own books on the demarcation problem in philosophy of science (Nonsense on Stilts and the forthcoming Philosophy of Pseudoscience) begin with the assumption that concepts such as “science” and “pseudoscience” are Wittgenstein-style family resemblance concepts. That doesn’t mean they cannot be refined, and nothing in the responses to Gettier’s cases implies that a non JTB definition of truth cannot follow in the same category of “fuzzy” concepts.

> you're characterising knowledge based on the consensus of reliable experts as "hearsay", which is not reasonable <

No, you were. I characterized knowledge on the basis of what experts (in epistemology) think it is.

> I would ask you whether you "know" that Manila is the capital of the Philippines. <

Again, yes in the common sense of the word, not necessarily in the technical one. I don’t see why you don’t want to make the distinction.

> we should not be surprised if it breaks down or becomes imprecise in more unusual cases, just as Newtonian physics is perfectly adequate and correct for its domain but doesn't work at very small scales or very high energies. <

Well, that’s an interest example, since physicists agree that Newtonian mechanics is wrong, and that’s why it breaks down when stretched.

> For the typical day to day use of the term, JTB is an adequate definition. <

I believe I say exactly that at the end of the post.

> I'm using JTB. I'm asserting that being told a fact by a reliable source can confer justification <

Yes, in the common sense, but not, I think, in the JTB. After all, you are invoking an authority whose reasonings and methods you don’t understand (hypothetically). You may be “justified” in doing so in the lay term of the sense, but not in the technical one.

Baron,

> Yes, in the long ago beginning you denied that anything, including humans, had a purpose. <

No, no, no. You keep confusing / equivocating between two very distinct meanings. Individual human beings of course have purposes. Humanity as a class does not. I *always* maintained the former, and *never* the latter. Keep you quotations straight, please.

Waldemar,

> provided we assume that the thought - I'm not even referring the brain, because it would be too obvious - is a function of perception <

No, thoughts are not necessarily functions of perception, you are arching back to an empiricist position that has not been taken seriously in philosophy since Kant.

> Marvin Minsky, who states that there's no distinction between emotions and thinking <

Wrong, emotions are a component of thought, but certainly not the only one.

As for the Singularity, here is what I think of it:http://rationallyspeaking.blogspot.com/2011/04/ray-kurzweil-and-singularity-visionary.htmlhttp://rationallyspeaking.blogspot.com/2009/11/david-chalmers-and-singularity-that.html

I certainly used Minsky's assumption off context: he meant the emotions are crucial in weaving the sense of self, the consciousness, and I don't see why it should not be so. Their connection with perception, in what I was exposing, comes from the observation that they are responses to what is perceived, their complements, and also perceived by the brain as objects. And what I intended to say is: as a model, perception seems to be useful to symbolize - to represent - the process through which the though is aware of its objects; we can't posit that it sees, hears, tastes them as the five senses do, although it's not impossible to consider this process as a different kind of perception, a perception that deals with sensations of images, sounds, textures, but not necessarily in the same way that they are acquired.

As for the thoughts being functions of perceptions, the idea behind it is that it's impossible to notice the former without the intercession of the latter - or that the thought can't even have a start without the senses. (Perhaps you, as a biologist, can tell more about this.) So, if reality is a fact (if solipsism is not true :)), it's supposed the thought have some possible connection with it, the so called innate knowledge, be it the idea of time-space, or the more selfish idea of good (the germ of ethics - or the way he behaves in the world).

Back to mathematical objects: isn't it simpler to figure out their conception as generalizations made on the data from senses than suppose that they come from a different place or that we just 'guess' them? Well, after transformed into more palatable objects to the thought, a subsequent appreciation of this result shows an indeed exquisite set of properties that these objects have.

A thing I cannot understand in this Platonic view of mathematical objects are the reasons its theorists have to suppose they are in a different reality. How long are we going to sustain the pointless debate on the nature of universals, for instance? They exist as they are, and are useful in the same way. There's no need to compose an 'image' of, say, 'human in general' to comprehend that it is an idea of a set of supposed properties. Also it seems to be perfectly explicable through the act of collation, from which it's likely to obtain what's similar and what's not. And as I said, as objects perceived by the thought itself while conceiving them, they are treated like any other objects of the senses and indeed are offered back to these latter in order to be better observed (not every one is able, like Tesla, for instance, to do all the work without the help of them). So, I don't see the point in calling Plato's ideas back.

I think you need to distinguish between modern mathematical platonism and Plato's orignal ideas of perfect forms. Modern mathematical platonism is much less silly.

Modern mathematical platonism does not require one to believe in an alternate dimension where mathematical objects are physical. It does not require one to believe that we know of these objects because our souls once existed in this plane of existence. Nobody takes those beliefs seriously any more, to my knowledge.

Instead, the central claim is that mathematical objects exist independently of human thought.

For me, it seems obvious that mathematical platonism is correct. If there is some mathematical problem we independently encounter and independently try to solve, we might independently come up with the same solution (e.g. Newton and Leibniz independently discovering many aspects of calculus). Clearly, neither of them can be the creator of calculus, and so calculus was not created. Rather, they both discovered it - it already (and has always) existed.

It's also obvious when you consider striking visual mathematical objects such as the Mandelbrot set. This set, discovered by Benoit Mandelbrot, has complexity and beauty that surprised its discoverer as he explored it. If he had created it or designed it, then it seems it could not have surprised him. Again, it seems clear that he did not create something that did not previously exist, but he was the first to discover it in the space of mathematical possibilities.

If you don't think that mathematical objects exist, then that's OK, but to me it signifies only that you have a narrower conception of existence than I do. If we constrain existence to apply only to physical, tangible objects, then mathematical objects do not exist. If we accept a broader definition, then they do.

In any case, it seems absolutely clear to me that mathematical objects do exist for some reasonable interpretations of existence.

Thanks for your help, but unhappily this is what I understand by mathematical Platonism. What is particular in my view (and I mostly blame my written English for my inability to state it convincingly) is that I understand the mathematical objects as derived from the experience and not as existing independently from it, derived in a similar way the universals are, from the same source, as just extrapolations any brains do (perhaps, in the case of the universals, due to a kind of biological incapacity of perceiving and naming each individual in the universe, our biological apparatus chooses to collect sets of properties shared by related sets of individuals). The matter is that as extrapolated objects they have, yes, properties that are, yes, amazing, mainly due to the facts that, first, any human being is able to grasp them (or is constrained to do so), and second, their properties are available to any theorization (in the old sense of consideration, observation) in an analogous way to the theorizing of objects perceived by the senses are.

Taking this Platonic view seriously, if one of the most important criteria of identification of those objects is, for instance, independence from the thought, then the objects perceived by the five senses must be Platonic too, as they are equally discovered, independent and never invented (I don't really believe in invention, a concept that scientifically has no meaning to me, designating just a kind of vanity analogous to some scientists' metaphors on 'discovering the logic of the creation' and so on - these later ones might be also simple poetic insights). I don't see the point in the argument of independence. Well, take note that I'm not saying that every mathematical object is an extrapolation of a precise object perceived by the five senses, but just of some of those objects, and the consideration of their properties, yes, is the process that gives birth to mathematics: those extrapolated objects have their properties extrapolated, thus coming into existence the remaining ones (this is also what Peirce calls infinite semiosis or, if not that, something very close to it, perhaps entailing that mathematics is indeed infinite or, better, 'transfinite', if we want to agree with Cantor). This is the reason I insist in that the thought is a kind - a very particular kind - of perception, because it indeed perceives its own extrapolations as objects and get different results from their observation. I don't really see the problem of thinking this way.

By the way: what would be the means those Platonic objects use to reach our thoughts? I ask this based in the impression that this smells a feeble disguise made to fit some kind of neo dualism. Philosophy seems to regularly hunt this kind of deadlock. I think it explains nothing and in addition hinders a more fruitful understanding on the nature of knowledge, if that exists.

It's very likely that my exposition is just a detailed explanation of my stupidity and inability to reach the heights of such a concept, but also a testimony of my effort to get there. One day, who knows?

Unfortunately, I'm having some difficulty grasping your position precisely. If I can summarise and paraphrase the main points, to my understanding you are claiming that:

1) Mathematical objects do not exist independently of humans, but are complex and often indirect extrapolations of our perceptions of the physical world, also you don't see why independence is important or relevant.

I disagree with this because I think the same mathematical truths and would likely be obtained by us even if our perceptions were very different. I think the same mathematical principles could hold for alien species on other planets or even in very different universes. They are, unlike pretty much anything else, entirely uncontingent on anything. They are all that is truly independent.

I may agree with you in practice that it would be very difficult for us to conceive of mathematical truths if we didn't have our perceptions, yet I think it is plausible that a hypothetical genius superhuman brain in a vat (e.g. an AI) could derive many mathematical truths even without any (sensory) perceptions whatsoever.

2) Physical object must also be platonic, because they are also discovered and not invented.

They're not platonic, but they exist and they exist independently of us. They're not platonic because they are physical - that's pretty much what is meant by platonic in this context.

3) Thought is a kind of perception

Ok. I'm reasonably happy to go along with that, but it seems to be a question of how we define "perception" rather than anything more substantive.

4) If platonic objects exist independently of the mind, then we need to account for how the mind can perceive them

This is actually relevant to the EAAN! If we evolved a mechanism to come to true beliefs, then mathematics is just a formalisation of this process. Our evolved machinery for acquiring true beliefs through careful deliberation therefore equips us to explore mathematical objects.

1) "I disagree with this because I think the same mathematical truths and would likely be obtained by us even if our perceptions were very different."

Perceptions of what? I was referring to mathematical objects, whose perception by us is supposed to provide the so called universal mathematical truths. I believe that if whatever odd being is able to perceive (or conceive if you prefer, to ease our way until I re-assume the idea of thought as a kind of perception) mathematical objects in the way we perceive them, it's indeed likely that he would deduce the same truths we get from them. Unless he perceives them differently, like a circle as a Mandelbrot set or vice-versa, I doubt that we could easily communicate with him on this matter, and I don't really know what this twisted perception could really be or mean. OK, the other hypothesis I conceive for your assumption on difference of perception is: our perceptions of those objects are different and even so we get the same truths: if this supposition goes along I will think you're telling me that those truths are independent of the mathematical objects, a feature I can't conceive.

Remember that I was talking about perception in the 'material' world, like the perception of the sun, followed by its extrapolation into a circle and then by the contemplation of this object inside the mind in order to get its truths. If an alien perceives the circle as a circle and starts to combine it with straight lines, for instance (provided they perceive straight lines as such), I don't see why he wouldn't get the same results we get. It's obvious that all this is a matter of time, for I'm also convinced that the simple presence of a circle and some straight lines is not able to instantly inspire no matter who and so magically provide him the truths.

2) Physical objects: "They're not platonic because they are physical"

In a materialistic context I can't understand this statement. Perhaps in Frege's time, when at least neuroscience was substantially different, I believe it's been still possible to conceive immaterial objects exclusively perceived by the thought. But now we can suppose a bit more, at least that there is some of the other part of the matter, some energy, I mean, doing some job all over the gray matter and a little beyond it. Are we still so bewitched by the properties of the thought that we mistakenly take what it probably is by its effects on us (on itself)? Until now we can't posit too much about it, and we must restrain ourselves to assumptions that can be made using those informations. Mathematical objects might also be a part of material world, although we can somehow perceive or feel them as if they were not.

3) I played a little with the idea of thought as perception, but I indeed think seriously this way. The approach seems straight forward to me: maybe because the thought manifests itself or even awakes by means of the senses, I believe its method of operation, by which means we are able to notice we're thinking, has strong influences from them; it's still possible that in truth we can't make a single image of a line with our thoughts, but we firmly believe we're seeing it (as a trained musician I experience sometimes the sensation of real, neat tones - not in my hearing, but - inside the brain, a sensation that disappears when I pay too close attention to it, thus returning the old impression or sensation of 'mute sounds', but sounds anyway, entirely useful to perform job tasks). So, we can't say that thought is precisely like this or that sense, for truly it is - or results from - at least the sum of all the senses (we don't have sufficient data to advance much more, I believe). So, this is why I feel comfortable in saying that either it is like a sense or - preferably - it is a different, special sense (the one that synthesizes the remaining five. I'm so sorry that this looks so spurious to some people.

So, forgive my ignorance, but please tell me how naturalism explains the way mathematical objects, being immaterial, are known to our brain and how it happens that they fit so well into the descriptions of the world that some people even believe the world is mathematically planned.

6) I also don't believe in the existence of theories that explain nothing: a failed theory can express a lot about the circumstances in which it was discovered , its proponents, a way of not producing theories etc (so, it talks still about the world).

Now I'm not concerned about what Math. Plat. explains or fails to explain, but about what it entails: the idea of transcendence, which could mean, in short, something it points to, whose existence we just suspect, not by means of some express sign of its very existence (if that was the case, it wouldn't be transcendent) but as just a tool to help in the understanding of something we don't understand yet (our ignorance). The problem with transcendence is that it rightfully comes into existence as a hypothesis that can be neither proved, nor disproved, then becoming a sort of resource of other suppositions (taken as truths, for they support the initial hypothesis), ultimately, a story we know very well the sequel.

On the other hand, the hypothesis of thought as a kind of perception would provide, I suppose, a common denominator to push other assumptions about the knowledge, for instance, that should be kept inside the limits of what can be said in the context of what is immanent, in Kantian sense.

Again, I'm finding it difficult to understand exactly where you're coming from, but I can tell you're an intelligent and intellectually honest person, so I'm going to try.

1) Same truths, different perceptions.

By different perceptions, I mean imagine if dolphins evolved and developed mathematics. They have a rich sense of sonar and think of their environment as a 3D space where they can navigate up or down freely. Their view of the world is quite different from ours, yet I think they would discover similar mathematical principles.

Or aliens in another universe where space is more obviously non-Euclidean. They might not discover Euclidean geometry for a long time, but they might eventually nonetheless just as we have discovered non-Euclidean geometries. The point is these concepts exist independently, waiting to be discovered. They are more than extrapolations of our perceptions.

Or a species with no visual sense or imagination at all. They can't visualise a circle the way we can, but that doesn't mean they can't develop the mathematical concept of a circle - a curve which is at all points equidistant from a center.

I think there's some simple misunderstanding here. What I mean by a "platonic" object is simply an abstract object that exists independently of the physical world. Physical objects fall outside of this category by definition. You seem to be using some other interpretation of the term, so I don't understand your confusion.

3) Thought as perceptionAgain, no problem. I think this is just a way of looking at it, but a perfectly valid way. I don't think it's spurious at all.

4/5) Interaction of platonic objects with physical brains

Mathematics is fundamental to both platonic objects and the physical world (which is governed by physical laws which are mathematical in nature). Since the physical world is mathematical and regular (and must be for naturalism to be true), it has been adaptive for us to evolve brains which have the ability to think consistently so as to interact with it successfully. But once you are thinking consistently, you are effectively doing mathematics, and you are discovering mathematical principles.

6) The utility of Mathematical Platonism

Seriously, check out the MUH. I'm convinced that mathematical platonism is the key to understanding why the universe exists, why it is fine-tuned for life and why it seems to be so surprisingly mathematical at a fundamental level.

I'm not sure I like words like "transcendence" which seems a bit too vague and mystical for my taste.

As you stated, "Mathematics is fundamental to both platonic objects and the physical world". And this is the point. How does it happen to be so? I guess that to answer this question, even Mathematical Platonism would have to invoke 'Plato's Platonism' :), and the problem with it is, however a truly marvelous piece of imagination, there's no way yet to test the existence of Plato's Idea as we test the existence of material things. So, either we endure this specific ignorance, or we decide to look for any suitable explanation at hand.

We have other mental objects whose origin raises no doubt to us: the so called universals, whose nature or form or whatever feature has been long debated and that, at last, come to be just collections of properties observed in some extant things and does not in necessity have to be conceived by us as if they possessed a shape imitating that of the objects whose properties they express. Universals is the name I'm incidentally giving here to what is sometimes called 'general concept', curiously approaching Plato's view on this term.In this case, the universals are not platonic, although the circle, for instance, is. Is it? If so, I don't agree with this. I just can't, since I observe that the circle I have in my mind is in several aspects too similar to the man that I also have there: however devoid of shapes, I take notice of them as sets of properties. Yes, you would say, but the origin of the universal man is the extant world and that of the circle is... what? I can't stand this doubt - if there is any I can.

The origins of the circle and of a great deal of mathematical objects can be traced back to the same world from where I took the universal 'man'. The circular shape is shared by several perceived objects and is easily explainable as a property of those individuals, a property we think so peculiar that we started to examine more closely. And this process we applied to the property 'circle' we use (or are able to use) to any property of, for instance, the universal 'man', like the intelligence, and to any possible trait of no matter what that we observe.

In fact mathematical objects reveal themselves properties that amaze us throughout History and the origins of some of them can't be easily traced back to the world like the circle's, the triangle's or the positive integers'. But those unknown origins can be traced back to those objects whose origins can be traced back to the world. And so, for instance, we can see the circle used in topology to help guessing other dimensions, as we can witness several properties of the universal 'man' being extrapolated into ethics.

Concerning the differing perceptions and the universal conception of mathematical objects, I consider that, if what I stated above is true, I mean, if some mathematical objects are generalizations made from extant objects, being the remaining ones derived from them, then beings with different perceptions and similar processing brains would very likely arrive at the same mathematical objects, although not in the way we do. I don't like to use the 'if... then' frame off certain limits, but let's go: if, for instance, this being sees what we call straight lines as curves, then it would be likely to suppose that it would start its geometry by some non-euclidean point of view and with time and due commitment it would arrive at the entire mathematics that we humans have.

And finally, I'm convinced that all the above said isn't harmful to any theory, even the one about the causes of the universe's existence.

>"Mathematics is fundamental to both platonic objects and the physical world". And this is the point. How does it happen to be so?<

Good question. One answered by the MUH! If the MUH is correct, the universe is a mathematical construct and so mathematics is fundamental. (Platonic objects are also mathematical constructs)

I'm not really on board with the idea of universals. They're too vaguely defined to have a solid ontological status. The universal 'man' for example is fine for typical men, but runs into trouble when you ask if it applies to edge cases such as foetuses, transsexuals (assuming you mean male humans), intersex individuals, human-animal hybrids, early hominids, discarded human skin cells, androids, humanoid aliens, simulated virtual people, dead men, comatose men, brain-dead men etc. Only universals which have been absolutely rigidly defined can be said to exist, and when they have been so defined they are instances of mathematical constructs.

That's the difference between the universal man and a circle. A circle has an absolutely precise mathematical definition. There is no edge case. Either something is a circle or it isn't. Something very close to a perfect circle is not actually a circle. In contrast, there is no definition of a perfect man.

I'd rather say that the mind is a very strange environment inside the world and like others produces odd species from no matter what it takes from its surroundings. Notwithstanding, it's as a worldly object as anything else. And has a perhaps standard feature: it doesn't deal very well with diversity, although has to endure some, and frequently punishes its owners when they try to overwhelm it with myriads of entities scattered around its empty shelves... :)

I'm not dismissing the debate. I just suggest we transfer it to another place, since the party here seems to be over. :(

Btw, if you don't mind, we could fill our respective blogs with the conversation. It'd look funny...

http://txtpub.blogspot.com.br/2013/07/disagreeable-mind-desagradavel-mente.html - just a pun!!

@Massimo, "Individual human beings of course have purposes. Humanity as a class does not."Apparently you don't see any contradictions there, and I ask again how individual humans acquired purposes while belonging to a class of biological beings who, in what seems to be your view, apparently as a whole evolved by accident.And of course when you take my alleged quotations out of context, asking me to keep them straight for your audience is at best ironic.

Doesn't adaptation suggest a kind of plasticity through which the organisms 'aim' to last? I can't conceive not just life, but also anything that can be individualized in the universe, without the 'purpose' (pardon me, I can't find a better substitute) of lasting long enough to be individualized: without duration there's no possible individuation. So, if I'm not completely mistaken, it should be comfortable enough to admit in the realm of life that its primary goal is survival, a feature that in the case of humans can assume oddly different meanings.

I think that it is never excessive to add to every consideration of the kind the assumption that we deal solely with thoughts, which are based on the data collected by the senses in reality, I mean, we will never be sure about what the world is really beyond the latter. The fact that our approaches work somehow can be ever seen as a mystery.

Adaptation suggests that the organisms are either intuitively or consciously self propelled, or programmed somehow by the nature that produced them, to change themselves on cue. If they are self propelled then they appear to have a purpose for adapting, which may well be to survive changes for another moment, and then the moment after that, until their strategic functions evolve through trial and error experiences of change to envision longer moments just as important to their survival as the shorter ones. But as Massimo would seem to have it, the accidents of nature have propelled organisms to initially react without a purpose, until they have somehow by miraculous accident attained the state of humanness, and then only purposefully reactive as individual humans rather than a class. Those individuals somehow being free to acquire purposes, yet not through any impetus of their cultural apparatus.

>but this is a point recognized by a number of philosophers since Wittgenstein.<

Hardly surprising! If I've given you the impression that I have a negative opinion of philosophers in general, then I certainly didn't mean to. I think I'm with Wittgenstein on this one.

>nothing in the responses to Gettier’s cases implies that a non JTB definition of truth [I assume you mean knowledge - Disagreeable Me] cannot follow in the same category of “fuzzy” concepts.<

I thought the whole idea of fuzzy concepts is that they defy precise definition? My point is that knowledge is such a fuzzy concept. Gettier did good work by showing this, but I think it's possible to reconcile this with JTB simply by recognising that knowledge is fuzzy and the concept breaks down in some corner cases.

>>> you're characterising knowledge based on the consensus of reliable experts as "hearsay", which is not reasonable <<

No, you were. I characterized knowledge on the basis of what experts (in epistemology) think it is.<

It took me a while to figure this out, but I see now. You misunderstood me. Let me edit my original sentence to clarify:

'you're characterising [knowledge based on the consensus of reliable experts] as (knowledge based on) "hearsay"'

To recap:

I claimed that one could be justified in trusting a reliable source such as the consensus of experts, e.g. on matters of physics. You referred to this as belief based on hearsay. I disagreed with this characterisation and then you followed this with the misunderstanding above.

>Again, yes in the common sense of the word, not necessarily in the technical one. I don’t see why you don’t want to make the distinction.<

I understand that people use terms loosely in casual conversation. However, in this discussion I am not discussing knowledge casually. I have been talking about the technical concept, defined as JTB. Again, according to the technical concept of knowledge, do you know that the capital of the Philippines is Manila? What would it take for you to know this? Perhaps it is impossible to know?

>Well, that’s an interest example, since physicists agree that Newtonian mechanics is wrong, and that’s why it breaks down when stretched.<

And yet they're perfectly happy to use it as a convenient simplification in contexts where it is sufficiently accurate. It breaks when stretched because it's not fundamental. Which is why it expresses perfectly my attitude towards the concept of knowledge. "Knowledge" is a convenient shorthand for JTB in contexts where that concept works. It doesn't apply in other contexts, where we would be better off talking in terms of more fundamental concepts such as truth and belief.

>You may be “justified” in doing so in the lay term of the sense, but not in the technical one.<

Hmm, well if we're not exploring the concept of justification, we're probably at an impasse. Until you explain what you mean by justification, I'm at a loss to understand you.

But again, what, essentially, is the difference between your trust of your eyes and my trust of a reliable source?

A thought experiment. Say you yourself researched the methods used to verify some very orthodox and universally accepted scientific finding, and then you reproduced the experiment yourself and found the same result. I think you would agree that your belief in the result is now justified.

However, what if you found a different result? I don't know about you, but I would trust the consensus and not the evidence of my own eyes. I would assume that I had made some kind of mistake and I would seek the aid of an expert in correcting me. Clearly, in some cases, the opinion of a reliable source is an even sounder basis for justification than one's own experience.

I am not sure I understand the point of the "dog in the park" example. The "justification" depends on going through the false lemma "What I saw was a dog": yes, the principle used to get there "my eyesight is generally reliable" is not false, but neither was "mail usually reflects the correct address of the person" false in the "Long Island" case.